P3.4-20. The input to the circuit shown in Figure P3.4-20 is the voltage source voltage V_s. The output is the voltage v_o. The output of this circuit is proportion to the input, that is

Figure P 3.4-20.

First combine the 6 resistors to the right into one effective resistance R_Eff1. The two on the right end in parallel will produce R/2. Then the three in series become 2.5 R which is now in parallel with the remaining resistor R

So

The circuit looks like

Now we can use voltage division to find

Ok, now expand the circuit so that only the right two resistors are joined and have an effective resistance of

Again apply voltage division to find v₀

Now plug in

So

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This page last updated on January 19, 2019